Premier said it was withdrawing support for an earlier offer from Swiss electro-mechanical engineering group Daetwyler AG (SWX:DAE), which valued it at £615mln.
Daetwyler had planned to merge Premier Farnell with its Daetwyler Technical Components UK division, resulting in a global technical parts business with about 4,900 staff and expected revenues of about £1.3bn.
Avnet said it believed a merger with Premier Farnell represented "a strong strategic fit and is highly attractive".
"Both companies share very similar strategic values and are highly complementary in terms of product range, distribution channels and geographic footprint," it said.
Premier Farnell directors, advised by investment bank Lazard and legal consultants Gibson Dunn, said they considered the financial terms of the transaction to be "fair and reasonable".